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From: JCH on 27 Jun 2010 10:50


"Fred Marshall" <fmarshallx(a)remove_the_xacm.org> schrieb im Newsbeitrag
news:W8qdnTL8DNNba7nRnZ2dnUVZ_rKdnZ2d(a)centurytel.net...
> fisico32 wrote:
>> Hello forum,
>>
>> if a time-invariant (zero memory) nonlinear filter is fed with a delta
>> impulse, it will output a certain output. That output will be the same no
>> matter when the impulse is applied due to
>> time invariance....
>>
>> Superposition (convolution) is not valid for nonlinear system.
>> Is there however some generalized impulse response concept for nonlinear
>> systems?
>>
>> After all, nonlinear system are locally linear....
>>
>
> You haven't really revealed your motivation so it's hard to be helpful
> without guessing. Impulses as inputs aren't usually real, thus not very
> interesting in practice - aside from all the nice analytical stuff you
> might do.
>
> The one thing that intrigued me long ago, and that I used very usefully,
> was the notion of "describing functions" for nonlinear system analysis and
> controls designs. You could look it up. More modern methods may apply
> but I can't help much with that. The idea is that it linearizes the
> nonlinear system for analysis purposes - based more on a lowpass
> assumption of the system rather than "local" linearities I believe.
>


One has a good chance for linearizing non-linear systems.

EXAMPLE

* http://home.arcor.de/janch/_control/20100627-(non)linear-system/


JCH



From: maury on 28 Jun 2010 14:12
On Jun 25, 11:26 am, "fisico32" <marcoscipioni1(a)n_o_s_p_a_m.gmail.com>
wrote:
> Hello forum,
>
> if a time-invariant (zero memory) nonlinear filter is fed with a delta
> impulse, it will output a certain output.
>
> That output will be the same no matter when the impulse is applied due to
> time invariance....
>
> Superposition (convolution) is not valid  for nonlinear system.
> Is there however some generalized impulse response concept for nonlinear
> systems?
>
> After all, nonlinear system are locally linear....

The accepted _generalized_ impulse response _concept_ is the Volterra
kernel. Look for work by Stephen Boyd of Stanford Univ. Some work on
Volterra kernels has been done lately, but Boyd's work is quite
definitive.

Maurice Givens

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